Modeling of time-dependent non-uniform dielectric breakdown using a clustering statistical approach

We report a time-dependent clustering model for non-uniform dielectric breakdown. Its area scaling and low-percentile scaling properties are rigorously investigated. While at high percentiles non-uniform area scaling dominates, the model restores the weakest-link characteristics at low percentiles relevant for reliability projection. As a result, we develop a comprehensive methodology for the parameter extraction and projection methodology for non-uniform dielectric breakdown. Excellent agreement is obtained between the model and the experimental data of back-end-of-line low-k dielectrics and front-end-of-line gate dielectrics, suggesting a wide range of applications of this model in the field of dielectric breakdown reliability. © 2013 AIP Publishing LLC.